zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Exp-function method and its application to nonlinear equations. (English) Zbl 1153.35384
Summary: Exp-function method is used to find a unified solution of a nonlinear wave equation. Variant Boussinesq equations are selected to illustrate the effectiveness and simplicity of the method. A generalized solitary solution with free parameters is obtained.

35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations
[1]He, J. H.: Variational iteration method – a kind of non-linear analytical technique: some examples, Int J non-linear mech 34, No. 4, 699-708 (1999)
[2]He, J. H.; Wu, X. H.: Construction of solitary solution and compacton-like solution by variational iteration method, Chaos, solitons & fractals 29, No. 1, 108-113 (2006) · Zbl 1147.35338 · doi:10.1016/j.chaos.2005.10.100
[3]He JH. Variational iteration method – Some recent results and new interpretations. J Comput Appl Math [in press]. · Zbl 1119.65049 · doi:10.1016/j.cam.2006.07.009
[4]He JH, Wu XH. Variational iteration method: new development and applications. Comput Math Appl [accepted]. · Zbl 1141.65372 · doi:10.1016/j.camwa.2006.12.083
[5]Odibat, Z. M.; Momani, S.: Application of variational iteration method to nonlinear differential equations of fractional order, Int J nonlinear sci numer simul 7, No. 1, 27-34 (2006)
[6]He, J. H.: New interpretation of homotopy perturbation method, Int J mod phys B 20, No. 18, 2561-2568 (2006)
[7]He, J. H.: Application of homotopy perturbation method to nonlinear wave equations, Chaos, solitons & fractals 26, No. 3, 695-700 (2005)
[8]He, J. H.: Limit cycle and bifurcation of nonlinear problems, Chaos, solitons & fractals 26, No. 3, 827-833 (2005) · Zbl 1093.34520 · doi:10.1016/j.chaos.2005.03.007
[9]He, J. H.: Homotopy perturbation method for bifurcation of nonlinear problems, Int J nonlinear sci numer simul 6, No. 2, 207-208 (2005)
[10]Rafei, M.; Ganji, D. D.: Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method, Int J nonlinear sci numer simul 7, No. 3, 321-328 (2006)
[11]Siddiqui, A. M.; Mahmood, R.; Ghori, Q. K.: Thin film flow of a third grade fluid on a moving belt by he’s homotopy perturbation method, Int J nonlinear sci numer simul 7, No. 1, 7-14 (2006)
[12]Siddiqui, A. M.; Ahmed, M.; Ghori, Q. K.: Couette and Poiseuille flows for non-Newtonian fluids, Int J nonlinear sci numer simul 7, No. 1, 15-26 (2006)
[13]Wazwaz, A. M.: The tanh method: solitons and periodic solutions for the dodd – bullough – Mikhailov and the tzitzeica – dodd – bullough equations, Chaos, solitons & fractals 25, 55-63 (2005) · Zbl 1070.35076 · doi:10.1016/j.chaos.2004.09.122
[14]Abdusalam, H. A.: On an improved complex tanh-function method, Int. J. Nonlinear sci. Numer. simul. 6, 99-106 (2005)
[15]Bai, C. L.; Zhao, H.: Generalized extended tanh-function method and its application, Chaos, solitons & fractals 27, 1026-1035 (2006) · Zbl 1088.35534 · doi:10.1016/j.chaos.2005.04.069
[16]Abdou, M. A.; Soliman, A. A.: Modified extended tanh-function method and its application on nonlinear physical equations, Phys lett A 353, No. 6, 487-492 (2006)
[17]Ibrahim, R. S.; El-Kalaawy, O. H.: Extended tanh-function method and reduction of nonlinear Schrödinger-type equations to a quadrature, Chaos, solitons & fractals 31, No. 4, 1001-1008 (2007) · Zbl 1139.35396 · doi:10.1016/j.chaos.2005.10.055
[18]El-Wakil, S. A.; Abdou, M. A.: New exact travelling wave solutions using modified extended tanh-function method, Chaos, solitons & fractals 31, No. 4, 840-852 (2007) · Zbl 1139.35388 · doi:10.1016/j.chaos.2005.10.032
[19]Elwakil, S. A.; El-Labany, S. K.; Zahran, M. A.; Sabry, R.: Modified extended tanh-function method and its applications to nonlinear equations, Appl math comput 161, No. 2, 403-412 (2005) · Zbl 1062.35082 · doi:10.1016/j.amc.2003.12.035
[20]Pedit, Franz; Wu, Hongyou: Discretizing constant curvature surfaces via loop group factorizations: the discrete sine- and sinh-Gordon equations, J geomet phys 17, No. 3, 245-260 (1995) · Zbl 0856.58020 · doi:10.1016/0393-0440(94)00044-5
[21]Wazwaz, A. M.: Exact solutions to the double sinh-Gordon equation by the tanh method and a variable separated ODE method, Comput math appl 50, No. 10 – 12, 1685-1696 (2005) · Zbl 1089.35534 · doi:10.1016/j.camwa.2005.05.010
[22]Zhao, Xiqiang; Wang, Limin; Sun, Weijun: The repeated homogeneous balance method and its applications to nonlinear partial differential equations, Chaos, solitons & fractals 28, No. 2, 448-453 (2006) · Zbl 1082.35014 · doi:10.1016/j.chaos.2005.06.001
[23]Feng, Zhaosheng: Comment on ”on the extended applications of homogeneous balance method”, Appl math comput 158, No. 2, 593-596 (2004) · Zbl 1061.35108 · doi:10.1016/j.amc.2003.10.003
[24]Zhang, Jie-Fang: Homogeneous balance method and chaotic and fractal solutions for the Nizhnik – Novikov – Veselov equation, Phys lett A 313, No. 5 – 6, 401-407 (2003) · Zbl 1040.35105 · doi:10.1016/S0375-9601(03)00803-X
[25]Fan, Engui; Zhang, Jian: Applications of the Jacobi elliptic function method to special-type nonlinear equations, Phys lett A 305, No. 6, 383-392 (2002) · Zbl 1005.35063 · doi:10.1016/S0375-9601(02)01516-5
[26]Hon, Y. C.; Fan, Engui: Uniformly constructing finite-band solutions for a family of derivative nonlinear Schrödinger equations, Chaos, solitons & fractals 24, No. 4, 1087-1096 (2005) · Zbl 1068.35156 · doi:10.1016/j.chaos.2004.09.055
[27]Fan, E.; Hon, Y. C.: Applications of extended tanh method to special types of nonlinear equations, Appl math comput 141, 351-358 (2003) · Zbl 1027.65128 · doi:10.1016/S0096-3003(02)00260-6
[28]Wang, M. L.; Li, X. Z.: Extended F-expansion method and periodic wave solutions for the generalized Zakharov equations, Phys lett A 343, 48-54 (2005) · Zbl 1181.35255 · doi:10.1016/j.physleta.2005.05.085
[29]Yomba, E.: The extended F-expansion method and its application for solving the nonlinear wave, CKGZ, GDS, DS and GZ equations, Phys lett A 340, 149-160 (2005) · Zbl 1145.35455 · doi:10.1016/j.physleta.2005.03.066
[30]Ren, Y. J.; Zhang, H. Q.: A generalized F-expansion method to find abundant families of Jacobi elliptic function solutions of the (2+1)-dimensional Nizhnik – Novikov – Veselov equation, Chaos, solitons & fractals 27, 959-979 (2006)
[31]Wang, D. S.; Zhang, H. Q.: Further improved F-expansion method and new exact solutions of konopelchenko – dubrovsky equation, Chaos, solitons & fractals 25, 601-610 (2005) · Zbl 1083.35122 · doi:10.1016/j.chaos.2004.11.026
[32]Yomba, E.: The extended Fan’s sub-equation method and its application to KdV – mkdv, BKK and variant Boussinesq equations, Phys lett A 336, 463-476 (2005) · Zbl 1136.35451 · doi:10.1016/j.physleta.2005.01.027
[33]Yomba, E.: The modified extended Fan sub-equation method and its application to (2+1)-dimensional dispersive long wave equation, Chaos, solitons & fractals 26, 785-794 (2005)
[34]He, J. H.: Some asymptotic methods for strongly nonlinear equations, Int J mod phys B 20, No. 10, 1141-1199 (2006) · Zbl 1102.34039 · doi:10.1142/S0217979206033796
[35]He, J. H.; Wu, X. H.: Exp-function method for nonlinear wave equations, Chaos, solitons & fractals 30, No. 3, 700-708 (2006) · Zbl 1141.35448 · doi:10.1016/j.chaos.2006.03.020
[36]Wu XH, He JH. Solitary solutions, periodic solutions and compacton-like solutions using Exp-function method. Comput Math Appl [accepted]. · Zbl 1143.35360 · doi:10.1016/j.camwa.2006.12.041
[37]He JH, Abdou MA. New periodic solutions for nonlinear evolution equations using Exp-function method, Chaos, Solitons amp; Fractals [in press, doi:10.1016/j.chaos.2006.05.072.].